1. Field of the Invention
The present invention pertains generally to methods used in the inversion of data, more particularly to the inversion of seismic data, and still more particularly to the full wave seismic inversion of seismic data without using a source term.
2. Description of the Relevant Art
Common seismic industry practice is that velocity structure is estimated by analyzing the travel time of a set of seismic signals. In cross hole and surface-to-borehole applications, typical approaches involve ray tracing in which the ray may be straight or curved depending on the degree of resolution desired, and more recently the Fresnel volume approach. The travel time approach is fundamentally a high-frequency approximation with a maximum resolution on the order of a wavelength, or a fraction (5%) of the well separation in some practical cases. The usefulness of the result obtained from the ray tomography may be limited if the objective is to better understand the petrophysical and hydrological ‘properties’ of the soil and rock: an increasingly important subject in characterizing petroleum and geothermal reservoirs, with potential environmental applications.
A better alternative to the travel time approach appears to be full waveform inversion. A number of recent studies on this subject suggest that full waveform inversion may provide improved resolution of velocity and density structures. Amplitude and phase information contained in the waveform are both sensitive to intrinsic energy loss of the propagating wave through dispersion, and to the petrophysical properties of the material through which the wave propagates. These sensitivities are utilized by full waveform analysis to form an attractive tool for investigating hydrological and petrophysical properties of a geophysical medium.
Full waveform inversion has a major impediment to easy implementation. In all field applications, the effective source waveform and the coupling of the medium between the source and the receiver are not very well understood. The effective source waveform and its coupling to the medium under study are generally taken together as a lumped “source term”. The source/medium coupling problem can be resolved to some extent by using a good velocity approximation in geophysical applications; however, the measured signal cannot generally be accurately calibrated, rendering full waveform inversion a technical challenge.